Gravitation Makes the World Go Round
Gravitational Force The Force of gravity is an attractive force felt between all objects that have mass. G=6.67x10-11 N m 2 /kg 2
Example 1: What is the Force of Gravity on Earth due to the Sun? Calculate the force of gravity on the Earth due to the sun given the following: Mass of the Sun: 1.99x10 30 kg Mass of Earth: 5.97x10 24 kg Radial Distance: 1.5x10 8 km
Example 2: The Mass of Mars Calculate the mass of Mars given the following: Mass of Sun: 1.99x10 30 kg Radial Distance: 2.28x10 8 km Force of Gravity of Mars on the Sun: 1.64x10 21 N
The Newton s (Mind) Cannon idea was not Newton s idea. Gravity being a force between ALL OBJECTS was Newton s idea. Newton's Cannon
The One Direction Until now Gravity pointed downward...but it really points inward
The One Direction Since the force of gravity is always pointed inward...gravity is a centripetal force!
Example 3: The Acceleration of Gravity Calculate the acceleration of gravity on the Earth given the following: Mass of Earth: 5.97x10 24 kg Radius of Earth: 6371 km
Example 4: The Orbital Speed of Earth How quickly is the Earth moving right now in its orbit around the sun? Mass of the Sun: 1.99x10 30 kg Mass of Earth: 5.97x10 24 kg Radial Distance: 1.5x10 8 km
Example 5: How Far is the Moon From Earth? Determine the distance the moon is from Earth given the following: Mass of Earth: 5.97x10 24 kg Mass of the moon: 7.35x10 22 kg Speed of moon in orbit: 1025 m/s
Homework/Classwork Worksheet There will be an additional 2 problems based on vertical loops posted online ALSO, if you do not have a grade for something in Genesis, I DON T HAVE IT! I will not hunt you down. Come see me.
Kepler s Laws of Planetary Motion discovery worksheet is done between these two lessons
Introduction to Kepler s Laws Discovery worksheet completed here: Kepler's Laws Applet
Kepler s Laws of Planetary Motion
Ellipses An ellipse is a geometric shape in which the sum of the distances from two foci is constant.
Focus A focus is one of the points from which the above distances are measured.
Semimajor Axis The distance from the center of an ellipse to the furthest point along the major axis of the ellipse.
Eccentricity Deviation of a curve or orbit from circularity
Period The amount of time it takes a planet to revolve once around the sun
Kepler s First Law: The Law of Ellipses The general shape of a planetary orbit is an ellipse. The sun is at one focus.
Kepler s Second Law: The Law of Areas Each triangular area is the same Planets move faster when they are closer to the sun than when they are farther away. e=0 e=0.35 e=0.70
Planetary Velocity Decreases as Planetary Distance Increases Another relationship that can be shown by using
Max/Min Orbital Velocities What are the maximum and minimum orbital velocities of earth in its rotation around the sun? o o minimum distance from sun r min =1.47x10 11 m maximum distance from sun r max =1.52x10 11 m
Kepler s Third Law: The Law of Harmonies T 2 /R 3 = constant = k Equation is normally written T 2 = kr 3 This relationship applies to any orbiting system o o Planets orbiting the sun Jupiter s moons orbiting Jupiter
Units Really matter for k What is k when T is measured in seconds and when R is measured in meters? An astronomical unit (AU) is a unit of distance equal to the semimajor axis of Earth. What is the value of k when T is measured in years and R in AU?
So what exactly is k? Yet again derivable from Verify that this new form of k yields the same results as on the previous slide.
Homework Slide Complete the worksheet ALSO, if you do not have a grade for something in Genesis, I DON T HAVE IT! I will not hunt you down. Come see me.
Geosynchronous Satellites
Geosynchronous Geo: of, or relating to Earth Synchronous: at the same time Geosynchronous: Having an orbital period that is synchronized with Earth s rotation.
Examples of Geosynchronous Orbits Satellites! o o o o o o o Telephone Television Weather Global positioning Radio Internet Military
Objects in orbit around Earth
Example 1: How Far Away Are Geosynchronous Satellites? How far above the Earth s Surface are these satellites? (Ans: 35864 km) Let s begin with (again)
Example 2: How Quickly Must Geosynchronous Satellites Travel? Finally, a calculation that involves another equation! (Ans: 3070 m/s)
Homework Calculate the distance above Mars surface a Geosynchronous satellite would have to be and with what speed it must move in order to maintain that orbit.